Is there any possibility to use linear photonic crystals as nonlinearly or nonlinear photonic crystals are only fabricated for application purpose.
Regarding your query, I would like to add that PCs can exhibit both properties. Depending of the beam profile, intensity, structural parameters, these properties can be tunable. For your guidance, some links are attached herewith.
a) Article Linear and Nonlinear Optical Properties of Colloidal Photonic Crystals
b) https://aip.scitation.org/doi/abs/10.1063/1.2787161?crawler=true&journalCode=jap
In general, photonic crystal exhibit linear behavior at the low levels of light intensity and nonlinear behavior at the high levels of light intensity. However, crystals differ in their nonlinear constants those respond to the light intensity. For example, some photonic crystal shows nonlinear behavior at light intensity of 10^4 W/cm2 while some other one shows nonlinear behavior at light intensity of 10^6 W/cm2. Therefore, it depends on the material from which this crystal is made. Theoretically, we write refractive index as: n=n0 + n1*I + n2*I^2 + ..., but practically, not all photonic crystals can have higher order terms of refractive index as they cannot hold high intensities of light to show the nonlinear behavior.
I recommend reading the attached book of Amnon Yariv for much more basic and precise description of nonlinearity in photonic crystals.
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